Exploring solutions for the negative-order modified Korteweg–de Vries equation with a self-consistent source corresponding to moving eigenvalues

We focus on investigating the negative-order modified Korteweg–de Vries equation with a special source. Based on the inverse scattering transform method, we derive the temporal dependency of scattering data for the Dirac operator with moving eigenvalues. We derive the multisoliton solution to considered problem using matrix triplet method and illustrate the wave behavior of solutions in both presence and absence of a source.

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